WITH
DR. WALLIS THE MATHEMATICIAN.
HOBBES'S passion for the study of Mathematics began late in
life--attempts to be an original discoverer--attacked by
WALLIS--various replies and rejoinders--nearly maddened by the
opposition he encountered--after four years of truce, the war
again renewed--character of HOBBES by Dr. WALLIS, a specimen of
invective and irony; serving as a remarkable instance how the
greatest genius may come down to us disguised by the arts of an
adversary--HOBBES'S noble defence of himself; of his own great
reputation; of his politics; and of his religion--a literary
stratagem of his--reluctantly gives up the contest, which lasted
twenty years.
The Mathematical War between HOBBES and the celebrated Dr. WALLIS is
now to be opened. A series of battles, the renewed campaigns of more
than twenty years, can be described by no term less eventful. Hobbes
himself considered it as a war, and it was a war of idle ambition, in
which he took too much delight. His "Amata Mathemata" became his
pride, his pleasure, and at length his shame. He attempted to maintain
his irruption into a province he ought never to have entered in
defiance, by "a new method;" but having invaded the powerful natives,
he seems to have almost repented the folly, and retires, leaving "the
unmanageable brutes" to themselves:
Ergo meam statuo non ultra perdere opellam
Indocile expectans discere posse pecus.
His language breathes war, while he sounds his retreat, and confesses
his repulse. The Algebraists had all declared against the Invader.
Wallisius contra pugnat; victusque videbar
Algebristarum Theiologumque scholis,
Et simul eductus Castris exercitus omnis
Pugnae securus Wallisianus ovat.
And,
Pugna placet vertor--
Bella mea audisti--&c.
So that we have sufficient authority to consider this Literary Quarrel
as a war, and a "Bellum Peloponnesiacum" too, for it lasted as long.
Political, literary, and even personal feelings were called in to heat
the temperate blood of two Mathematicians.
What means this tumult in a Vestal's veins?
Hobbes was one of the many victims who lost themselves in squaring the
circle, and doubling the cube. He applied, late in life, to
mathematical studies, not so much, he says, to learn the subtile
demonstrations of its figures, as to acquire those habits of close
reasoning, so useful in the discovery of new truths, to prove or to
refute. So justly he reasoned on mathematics; but so ill he practised
the science, that it made him the most unreasonable being imaginable,
for he resisted mathematical demonstration, itself![380]
His great and original character could not but prevail in everything
he undertook; and his egotism tempted him to raise a name in the world
of Science, as he had in that of Politics and Morals. With the ardour
of a young mathematician, he exclaimed, "_Eureka!_" "I have found it."
The quadrature of the circle was indeed the common Dulcinea of the
Quixotes of the time; but they had all been disenchanted. Hobbes alone
clung to his ridiculous mistress. Repeatedly confuted, he was
perpetually resisting old reasonings and producing new ones. Were only
genius requisite for an able mathematician, Hobbes had been among the
first; but patience and docility, not fire and fancy, are necessary.
His reasonings were all paralogisms, and he had always much to say,
from not understanding the subject of his inquiries.
When Hobbes published his "De Corpore Philosophico," 1655, he there
exulted that he had solved the great mystery. Dr. Wallis, the Savilian
professor of mathematics at Oxford,[381] with a deep aversion to
Hobbes's political and religious sentiments, as he understood them,
rejoiced to see this famous combatant descending into his own arena.
He certainly was eager to meet him single-handed; for he instantly
confuted Hobbes, by his "Elenchus Geometriae Hobbianae." Hobbes, who saw
the newly-acquired province of his mathematics in danger, and which,
like every new possession, seemed to involve his honour more than was
necessary, called on all the world to be witnesses of this mighty
conflict. He now published his work in English, with a sarcastic
addition, in a magisterial tone, of "_Six Lessons to the Professors of
Mathematics in Oxford_." These were Seth Ward[382] and Wallis, both no
friends to Hobbes, and who hungered after him as a relishing morsel.
Wallis now replied in English, by "Due Correction for Mr. Hobbes, or
School-discipline for not saying his Lessons Right," 1656. That part
of controversy which is usually the last had already taken place in
their choice of phrases.[383]
In the following year the campaign was opened by Hobbes with
"~STIGMAI~; or, _marks_ of the absurd Geometry, _rural Language_,
Scottish Church-politics, and Barbarisms, of John Wallis." Quick was
the routing of these fresh forces; not one was to escape alive! for
Wallis now took the field with "Hobbiani Puncti dispunctio! or, the
undoing of Mr. Hobbes's Points; in answer to Mr. Hobbes's ~STIGMAI~,
_id est_, Stigmata Hobbii." Hobbes seems now to have been reduced to
great straits; perhaps he wondered at the obstinacy of his adversary.
It seems that Hobbes, who had been used to other studies, and who
confesses all the algebraists were against him, could not conceive a
point to exist without quantity; or a line could be drawn without
latitude; or a superficies be without depth or thickness; but
mathematicians conceive them without these qualities, when they exist
abstractedly in the mind; though, when for the purposes of science
they are produced to the senses, they necessarily have all the
qualities. It was understanding these figures, in the vulgar way,
which led Hobbes into a labyrinth of confusions and absurdities.[384]
They appear to have nearly maddened the clear and vigorous intellect
of our philosopher; for he exclaims, in one of these writings:--
"I alone am mad, or they are all out of their senses: so that no third
opinion can be taken, unless any will say that we are all mad."
Four years of truce were allowed to intervene between the next battle;
when the irrefutable Hobbes, once more collecting his weak and his
incoherent forces, arranged them, as well as he was able, into "Six
Dialogues," 1661. The utter annihilation he intended for his
antagonist fell on himself. Wallis borrowing the character of "The
Self-tormentor" from Terence, produced "Hobbius Heauton-timorumenos
(Hobbes the Self-tormentor); or, a Consideration of Mr. Hobbes's
Dialogues; addressed to Robert Boyle," 1662.
This attack of Wallis is of a very opposite character to the arid
discussion of abstract blunders in geometry. He who began with points,
and doubling the cube, and squaring the circle, now assumes a loftier
tone, and carrying his personal and moral feelings into a mere
controversy between two idle mathematicians, he has formed a solemn
invective, and edged it with irony. I hope the reader has experienced
sufficient interest in the character of Hobbes to read the long, but
curious extract I shall now transcribe, with that awe and reverence
which the old man claims. It will show how even the greatest genius
may be disguised, when viewed through the coloured medium of an
adversary. One is, however, surprised to find such a passage in a
mathematical work.
"He doth much improve; I mean he doth, _proficere in pejus_; more,
indeed, than I could reasonably have expected he would have
done;--insomuch, that I cannot but profess some relenting thoughts
(though I had formerly occasion to use him somewhat coarsely), to
see an old man thus fret and torment himself to no purpose. You,
too, should pity your antagonist; not as if he did deserve it, but
because he needs it; and as Chremes, in Terence, of his Senex, his
self-tormenting Menedemus--
Cum videam miserum hunc tam excruciarier
Miseret me ejus. Quod potero adjutabo senem.
"Consider the temper of the man, to move your pity; a person _extremely
passionate and peevish, and wholly impatient of contradiction_. A
temper which, whether it be a greater fault or torment (to one who must
so often meet with what he is so ill able to bear), is hard to say.
"And to this fretful humour you must add another as bad, which feeds
it. You are therefore next to consider him as _one highly opinionative
and magisterial_. _Fanciful_ in his conceptions, and deeply enamoured
with those _phantasmes_, without a rival. He doth not spare to
profess, upon all occasions, how incomparably he thinks himself to
have _surpassed all_, ancient, modern, schools, academies, persons,
societies, philosophers, divines, heathens, Christians; how despicable
he thinks all their writings in comparison of his; and what hopes he
hath, that, by _the sovereign command of some absolute prince, all
other doctrines being exploded, his new dictates should be_
_peremptorily imposed, to be alone taught in all schools and pulpits,
and universally submitted to_. To recount all which he speaks of
himself _magnificently_, and _contemptuously_ of others, would fill a
volume. Should some idle person read over all his books, and
collecting together his arrogant and supercilious speeches, applauding
himself, and despising all other men, set them forth in one
_synopsis_, with this title, _Hobbius de se_--what a pretty piece of
pageantry this would make!
"The admirable sweetness of your own nature has not given you the
experience of such a temper: yet your contemplation must have needs
discerned it, in those symptoms which you have seen it work in others,
like the strange effervescence, ebullition, fumes, and fetors, which
you have sometimes given yourself the content to observe, in some
active _acrimonious_ chymical _spirits_ upon the injection of some
contrariant _salts_ strangely vexing, fretting, and tormenting itself,
while it doth but administer _sport_ to the unconcerned spectator.
Which temper, being so eminent in the person we have to deal with,
your generous nature, which cannot but pity affliction, how much
soever deserved, must needs have some compassion for him: who, besides
those exquisite _torments_ wherewith he doth afflict himself, like
that
----quo Siculi non invenere Tyranni
Tormentum majus--
is unavoidably exposed to those two great _mischiefs_; an incapacity
to be _taught what he doth not know_, or to be _advised when he thinks
amiss_; and moreover, to this _inconvenience_, that he must never
_hear his faults but from his adversaries_; for those who are willing
to be reputed _friends_ must either not advertise what they see amiss,
or incommode themselves.
"But, you will ask, what need he thus torment himself? What need of
pity? If _he have hopes_ to be admitted the _sole dictator in
philosophy_, civil and natural, in schools and pulpits, and to be
owned as the only _magister sententiarum_, what would he have more?
"True, _if he have_; but what _if he have not_? That he _had_ some
hopes of such an honour, he hath not been sparing to let us know, and
was providing against the _envy_ that might attend it (_nec deprecabor
invidiam, sed augendo, ulciscar_, was his resolution); but I doubt
these hopes are at an end. He did not find (as he expected) that the
_fairies and hobgoblins_ (for such he reputes all that went before
him) did vanish presently, upon the first appearance of his
_sunshine_: and, which is worse, while he was on the one side guarding
himself against _envy_, he is, on the other side, unhappily
_surprised_ by a worse enemy, called _contempt_, and with which he is
less able to grapple.
"I forbear to mention (lest I might seem to reproach that age which I
reverence) the _disadvantages_ which he may sustain by his old age.
'Tis possible that time and age, in a person somewhat _morose_, may
have riveted faster that preconceived opinion of his own worth and
excellency beyond others. 'Tis possible, also, that he may have
_forgotten_ much of what once he knew. He may, perhaps, be sometimes
more _secure_ than _safe_; while trusting to what he thinks a firm
foundation, his footing fails him; nor always so vigilant or
quicksighted as to discern the _incoherence_ or _inconsequence_ of his
own discourses; unwilling, notwithstanding, to make use of the eyes of
other men, lest he should seem thereby to disparage his own; but
certainly (though his _will_ may be as good as ever) his _parts_ are
less vegete and nimble, as to _invention_ at least, than in his
younger days.
"While he had endeavoured only to _raise an expectation_, or put the
world in hopes of what great things he had in hand (_to render all
philosophy as clear and certain as Euclid's Elements_), if he had then
_died_, it might, perhaps, have been thought by some that the world
had been deprived of _a great philosopher_, and learning sustained an
invaluable loss, by the abortion of _so desired a piece_. But since
that _Partus Montis_ is come to light, and found to be no more than
what little animals have brought forth, and that _deformed_ enough and
_unamiable_, he might have sooner gone off the stage with more
advantage than now he is like to do; such is the misfortune for a man
to _outlive his reputation_!
"By this time, perhaps, you may see cause to _pity_ him while you see
him _falling_. But if you consider him _tumbling headlong_ from so
great a height, 'twill make some addition to that _compassion_ which
doth already begin to work. You are therefore next to consider that
when, upon the account of _geometry_, he was unsafely mounted to that
height of vanity, he did unhappily fall into the hands of two
mathematicians, who have used him so unmercifully as would have put a
person of _greater patience_ into _passion_, and meeting with such a
_temper_, have so discomposed him that he hath ever since _talked
idly_: and to augment the grief, these mathematicians were both
divines--he had rather have fallen by any other hand. These
_mathematical divines_ (a term which he had thought incomponible)
began to unravel the wrong end; and while he thought they should have
first _untiled the roof_, and by degrees gone downward, they strike at
the _foundation_, and make the building tumble all at once; and that
in such confusion, that by dashing one part against another, they make
each help to destroy the whole. They first fall upon his _last
reserve_, and rout his _mathematics_ beyond a possibility of
_rallying_; and by _firing his magazine_ upon the first assault, make
his own weapons _fight against him_. Not contented herewith, they
enter the _breach_, and pursue the _rout_ through his Logics, Physics,
Metaphysics, Theology, where they find all in confusion."
This invective and irony from this celebrated mathematician, so much
out of the path of his habitual studies, might have proved a
tremendous blow; but the genius of Hobbes was invulnerable to mere
human opposition, unless accompanied by the supernatural terrors of
penal fires or perpetual dungeons. Our hero received the whole
discharge of this battering train, and stood invulnerable, while he
returned the fire in "Considerations upon the Reputation, Loyalty,
Manners, and Religion of Thomas Hobbes, of Malmesbury, written by way
of Letter to a learned person, Dr. Wallis," 1662.
It is an extraordinary production. His lofty indignation retorts on
the feeble irony of his antagonist with keen and caustic accusations;
and the green strength of youth was still seen in the old man whose
head was covered with snows.
From this spirited apology for himself I shall give some passages.
Hobbes thus replied to Dr. Wallis, who affected to consider the old
man as a fit object for commiseration.
"You would make him contemptible, and move Mr. Boyle to pity him. This
is a way of railing too much beaten to be thought witty: besides, 'tis
no argument of your contempt to spend upon him so many angry lines, as
would have furnished you with a dozen of sermons. If you had in good
earnest despised him, you would have let him alone, as he does Dr.
Ward, Mr. Baxter, Pike, and others, that have reviled him as you do.
As for his reputation beyond the seas, it fades not yet; and because,
perhaps, you have no means to know it, I will cite you a passage of an
epistle written by a learned Frenchman to an eminent person in
France, in a volume of epistles." Hobbes quotes the passage at length,
in which his name appears joined with Galileo, Descartes, Bacon, and
Gassendi.
In reply to Wallis' sarcastic suggestion that an idle person should
collect together Hobbes's arrogant and supercilious speeches
applauding himself, under one title, _Hobbius de se_, he says--
"Let your idle person do it; Mr. Hobbes shall acknowledge them under
his hand, and be commended for it, and you scorned. A certain Roman
senator having propounded something in the assembly of the people,
which they, misliking, made a noise at, boldly bade them hold their
peace, and told them he knew better what was good for the commonwealth
than all they; and his words are transmitted to us as an argument of
his virtue; _so much do truth and vanity alter the complexion of
self-praise_. You can have very little skill in morality, that cannot
see the justice of commending a man's self, as well as of anything
else, in his own defence; and it was want of prudence in you to
constrain him to a thing that would so much displease you.
"When you make his _age_ a reproach to him, and show no cause that
might impair the faculties of his mind, but only age, I admire how you
saw not that you reproached all old men in the world as much as him,
and warranted all young men, at a certain time which they themselves
shall define, to call you _fool_! Your dislike of old age you have
also otherwise sufficiently signified, in venturing so fairly as you
have done to escape it. But that is no great matter to one that hath
so many marks upon him of much greater reproaches. By Mr. Hobbes's
calculation, that derives prudence from experience, and experience
from age, you are a very young man; but, by your own reckoning, you
are older already than Methuselah.
"During the late trouble, who made both Oliver and the people mad but
the preachers of your principles? But besides the wickedness, see the
folly of it. You thought to make them mad, but just to such a degree
as should serve your own turn; that is to say, mad, and yet just as
wise as yourselves. Were you not very imprudent to think to govern
madness?"--p. 15.
"The king was hunted as a partridge in the mountains, and though the
hounds have been hanged, yet the hunters were as guilty as they, and
deserved no less punishment. And the decypherers (Wallis had
decyphered the royal letters),[385] and all that blew the horn, are to
be reckoned among the hunters. Perhaps you would not have had the prey
killed, but rather have kept it tame. And yet who can tell? I have
read of few kings deprived of their power by their own subjects that
have lived any long time after it, for reasons that every man is able
to conjecture."